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Previous year question hub

Hyperbola - Coordinate Geometry - Mathematics Previous Year Questions

Practice Hyperbola - Coordinate Geometry - Mathematics previous year questions organised from real papers, with year-wise coverage and clear topic navigation.

23Papers
18Years
28Questions
1Topics

Hyperbola question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Hyperbola. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Medium 19 63.3%
Hard 6 20%
Not classified 3 10%
Easy 2 6.7%

Question type distribution

MCQ, numerical, multiple-select and other formats found in these papers.

Multiple Choices 25 83.3%
Numerical Answer Type (NAT) 3 10%
Subjective 2 6.7%

Subject weightage

Top subjects by unique question coverage.

Mathematics
28 Qs

Most asked topics

Top topics across the included previous year papers.

Coordinate Geometry
28 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Hyperbola
28 Qs

Paper coverage

Question coverage for the most populated papers. Every active PYP paper remains listed below.

JEE Advanced 2026 Paper 1 Online
1 Qs
JEE Advanced 2026 Paper 1 Online
1 Qs
JEE Advanced 2026 Paper 1 Online
1 Qs
JEE Advanced 2026 Paper 2 Online
1 Qs
JEE ADVANCED 2022 PAPER 2 ONLINE
1 Qs
JEE ADVANCED 2020 PAPER 2 OFFLINE
1 Qs
JEE ADVANCED 2018 PAPER 2 OFFLINE
2 Qs
JEE ADVANCED 2017 PAPER 1 OFFLINE
3 Qs
JEE ADVANCED 2015 PAPER 2 OFFLINE
1 Qs
IIT JEE 2012 PAPER 1 OFFLINE
1 Qs
IIT JEE 2011 PAPER 1 OFFLINE
1 Qs
IIT JEE 2011 PAPER 2 OFFLINE
1 Qs
IIT JEE 2010 PAPER 1 OFFLINE
3 Qs
IIT JEE 2008 PAPER 2 OFFLINE
1 Qs
IIT JEE 2007 PAPER 1 OFFLINE
1 Qs
IIT JEE 2006
1 Qs
IIT JEE 2005
1 Qs
IIT JEE 2005 MAINS
1 Qs
IIT JEE 2004 SCREENING
1 Qs
IIT JEE 2003 SCREENING
1 Qs
IIT JEE 1999
2 Qs
IIT JEE 1998
1 Qs
IIT JEE 1981
2 Qs

Included previous year papers

Newest papers appear first. Sort by year, question coverage or name.

PaperYear / sessionQuestions in this viewOpen
JEE Advanced 2026 Paper 1 Online20261View paper
JEE Advanced 2026 Paper 1 Online20261View paper
JEE Advanced 2026 Paper 1 Online20261View paper
JEE Advanced 2026 Paper 2 Online20261View paper
JEE ADVANCED 2022 PAPER 2 ONLINE20221View paper
JEE ADVANCED 2020 PAPER 2 OFFLINE20201View paper
JEE ADVANCED 2018 PAPER 2 OFFLINE20182View paper
JEE ADVANCED 2017 PAPER 1 OFFLINE20173View paper
JEE ADVANCED 2015 PAPER 2 OFFLINE20151View paper
IIT JEE 2012 PAPER 1 OFFLINE20121View paper
IIT JEE 2011 PAPER 1 OFFLINE20111View paper
IIT JEE 2011 PAPER 2 OFFLINE20111View paper
IIT JEE 2010 PAPER 1 OFFLINE20103View paper
IIT JEE 2008 PAPER 2 OFFLINE20081View paper
IIT JEE 2007 PAPER 1 OFFLINE20071View paper
IIT JEE 200620061View paper
IIT JEE 200520051View paper
IIT JEE 2005 MAINS20051View paper
IIT JEE 2004 SCREENING20041View paper
IIT JEE 2003 SCREENING20031View paper
IIT JEE 199919992View paper
IIT JEE 199819981View paper
IIT JEE 198119812View paper

All Hyperbola previous year questions

Practice every matching question in batches of 20, with every available option.

1
1981 · Mathematics · Coordinate Geometry · Hyperbola
IIT JEE 1981
The equation \({{{x^2}} \over {1 - r}} - {{{y^2}} \over {1 + r}} = 1,\,\,\,\,r > 1\) represents
A
an ellipse
B
a hyperbola
C
a circle
D
none of these
Open complete paper
2
1981 · Mathematics · Coordinate Geometry · Hyperbola
IIT JEE 1981
Each of the four inequalties given below defines a region in the \(xy\) plane. One of these four regions does not have the following property. For any two points \(\left( {{x_1},{y_1}} \right)\) and \(\left( {{x_2},{y_2}} \right)\) in the region, the point \(\left( {{{{x_1} + {x_2}} \over 2},{{{y_1} + {y_2}} \over 2}} \right)\) is also in the region. The inequality defining this region is
A
\({x^2} + 2{y^2} \le 1\)
B
Max \(\left\{ {\left| x \right|,\left| y \right|} \right\} \le 1\)
C
\({x^2} - {y^2} \le 1\)
D
\({y^2} - x \le 0\)
Open complete paper
3
1998 · Mathematics · Coordinate Geometry · Hyperbola
IIT JEE 1998
The angle between a pair of tangents drawn from a point \(P\) to the parabola \({y^2} = 4ax\) is \({45^ \circ }\). Show that the locus of the point \(P\) is a hyperbola.
Write your response
Open complete paper
4
1999 · Mathematics · Coordinate Geometry · Hyperbola
IIT JEE 1999
Let \(P\) \(\left( {a\,\sec \,\theta ,\,\,b\,\tan \theta } \right)\) and \(Q\) \(\left( {a\,\sec \,\,\phi ,\,\,b\,\tan \,\phi } \right)\), where \(\theta + \phi = \pi /2,\), be two points on the hyperbola \({{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1\).

If \((h, k)\) is the point of intersection of the normals at \(P\) and \(Q\), then \(k\) is equal to

A
\({{{a^2} + {b^2}} \over a}\)
B
\(- \left( {{{{a^2} + {b^2}} \over a}} \right)\)
C
\({{{a^2} + {b^2}} \over b}\)
D
\(- \left( {{{{a^2} + {b^2}} \over b}} \right)\)
Open complete paper
5
1999 · Mathematics · Coordinate Geometry · Hyperbola
IIT JEE 1999
If \(x\) \(=\) \(9\) is the chord of contact of the hyperbola \({x^2} - {y^2} = 9,\) then the equation of the vcorresponding pair of tangents is
A
\(9{x^2} - 8{y^2} + 18x - 9 = 0\)
B
\(9{x^2} - 8{y^2} - 18x + 9 = 0\)
C
\(9{x^2} - 8{y^2} - 18x - 9 = 0\)
D
\(9{x^2} - 8{y^2} + 18x + 9 = 0\)
Open complete paper
6
2003 · Mathematics · Coordinate Geometry · Hyperbola
IIT JEE 2003 SCREENING
For hyperbola \({{{x^2}} \over {{{\cos }^2}\alpha }} - {{{y^2}} \over {{{\sin }^2}\alpha }} = 1\) which of the following remains constant with change in \('\alpha '\)
A
abscissae of vertices
B
abscissae of foci
C
eccentricity
D
directrix
Open complete paper
7
2004 · Mathematics · Coordinate Geometry · Hyperbola
IIT JEE 2004 SCREENING
If the line \(62x + \sqrt 6 y = 2\) touches the hyperbola \({x^2} - 2{y^2} = 4\), then the point of contact is
A
\(\left( { - 2,\,\sqrt 6 } \right)\)
B
\(\left( { - 5,\,2\sqrt 6 } \right)\)
C
\(\left( {{1 \over 2},{1 \over {\sqrt 6 }}} \right)\)
D
\(\left( {4, - \,\sqrt 6 } \right)\)
Open complete paper
8
2005 · Mathematics · Coordinate Geometry · Hyperbola
IIT JEE 2005
Tangents are drawn from any point on the hyperbola \({{{x^2}} \over 9} - {{{y^2}} \over 4} = 1\) to the circle \({x^2} + {y^2} = 9\).Find the locus of mid-point of the chord of contact.
Write your response
Open complete paper
9
2005 · Mathematics · Coordinate Geometry · Hyperbola
IIT JEE 2005 MAINS

Tangents are drawn from any point on the hyperbola \(\frac{x^{2}}{9}-\frac{y^{2}}{4}=1\) to the circle \(x^{2}+y^{2}=9\). Find the locus of mid-point of the chord of contact.

A
\({{{x^2}} \over 4} + {{{y^2}} \over 9} = {{{{({x^2} + {y^2})}^2}} \over {81}}\)
B
\({{{x^2}} \over 4} - {{{y^2}} \over 9} = {{{{({x^2} + {y^2})}^2}} \over {81}}\)
C
\({{{x^2}} \over 9} + {{{y^2}} \over 4} = {{{{({x^2} + {y^2})}^2}} \over {81}}\)
D
\({{{x^2}} \over 9} - {{{y^2}} \over 4} = {{{{({x^2} + {y^2})}^2}} \over {81}}\)
Open complete paper
10
2006 · Mathematics · Coordinate Geometry · Hyperbola
IIT JEE 2006

If a hyperbola passes through the focus of the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ and its transverse and conjugate axes coincide with the major and minor axes of the ellipse, and the product of eccentricities is 1 , then

A

the equation of hyperbola is $\frac{x^2}{9}-\frac{y^2}{16}=1$

B

the equation of hyperbola is $\frac{x^2}{9}-\frac{y^2}{25}=1$

C

focus of hyperbola is $(5,0)$

D

focus of hyperbola is $(5 \sqrt{3}, 0)$

Open complete paper
11
2007 · Mathematics · Coordinate Geometry · Hyperbola
IIT JEE 2007 PAPER 1 OFFLINE

A hyperbola, having the transverse axis of the length \(2\sin \theta\), is confocal with the ellipse \(3{x^2} + 4{y^2} = 12\). Then its equation is

A
\({x^2}\cos e{c^2}\theta - {y^2}{\sec ^2}\theta = 1\)
B
\({x^2}{\sec ^2}\theta - {y^2}\cos e{c^2}\theta = 1\)
C
\({x^2}{\sin ^2}\theta - {y^2}{\cos ^2}\theta = 1\)
D
\({x^2}{\cos ^2}\theta - {y^2}{\sin ^2}\theta = 1\)
Open complete paper
12
2008 · Mathematics · Coordinate Geometry · Hyperbola
IIT JEE 2008 PAPER 2 OFFLINE
Consider a branch of the hyperbola \({x^2} - 2{y^2} - 2\sqrt 2 x - 4\sqrt 2 y - 6 = 0\)

with vertex at the point \(A\). Let \(B\) be one of the end points of its latus rectum. If \(C\) is the focus of the hyperbola nearest to the point \(A\), then the area of the triangle \(ABC\) is

A
\(1 - \sqrt {{2 \over 3}}\)
B
\(\sqrt {{3 \over 2}} - 1\)
C
\(1 + \sqrt {{2 \over 3}}\)
D
\(\sqrt {{3 \over 2}} + 1\)
Open complete paper
13
2010 · Mathematics · Coordinate Geometry · Hyperbola
IIT JEE 2010 PAPER 1 OFFLINE

The line \(2x + y = 1\) is tangent to the hyperbola \({{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1\).

If this line passes through the point of intersection of the nearest directrix and the \(x\)-axis, then the eccentricity of the hyperbola is

Enter a numerical response
Open complete paper
14
2010 · Mathematics · Coordinate Geometry · Hyperbola
IIT JEE 2010 PAPER 1 OFFLINE
The circle \({x^2} + {y^2} - 8x = 0\) and hyperbola \({{{x^2}} \over 9} - {{{y^2}} \over 4} = 1\) intersect at the points \(A\) and \(B\).

Equation of a common tangent with positive slope to the circle as well as to the hyperbola is

A
\(2x - \sqrt {5y} - 20 = 0\)
B
\(2x - \sqrt {5y} + 4 = 0\)
C
\(3x - 4y + 8 = 0\)
D
\(4x - 3y + 4 = 0\)
Open complete paper
15
2010 · Mathematics · Coordinate Geometry · Hyperbola
IIT JEE 2010 PAPER 1 OFFLINE
The circle \({x^2} + {y^2} - 8x = 0\) and hyperbola \({{{x^2}} \over 9} - {{{y^2}} \over 4} = 1\) intersect at the points \(A\) and \(B\).

Equation of the circle with \(AB\) as its diameter is

A
\({x^2} + {y^2} - 12x + 24 = 0\)
B
\({x^2} + {y^2} + 12x + 24 = 0\)
C
\({x^2} + {y^2} + 24x - 12 = 0\)
D
\({x^2} + {y^2} - 24x - 12 = 0\)
Open complete paper
16
2011 · Mathematics · Coordinate Geometry · Hyperbola
IIT JEE 2011 PAPER 1 OFFLINE
Let the eccentricity of the hyperbola \({{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1\) be reciprocal to that of the ellipse \({x^2} + 4{y^2} = 4\). If the hyperbola passes through a focus of the ellipse, then
A
the equation of the hyperbola is \({{{x^2}} \over 3} - {{{y^2}} \over 2} = 1\)
B
a focus of the hyperbola is \((2, 0)\)
C
theeccentricity of the hyperbola is \(\sqrt {{5 \over 3}}\)
D
The equation of the hyperbola is \({x^2} - 3{y^2} = 3\)
Open complete paper
17
2011 · Mathematics · Coordinate Geometry · Hyperbola
IIT JEE 2011 PAPER 2 OFFLINE
Let \(P(6, 3)\) be a point on the hyperbola \({{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1\). If the normal at the point \(P\) intersects the \(x\)-axis at \((9, 0)\), then the eccentricity of the hyperbola is
A
\(\sqrt {{5 \over 2}}\)
B
\(\sqrt {{3 \over 2}}\)
C
\({\sqrt 2 }\)
D
\({\sqrt 3 }\)
Open complete paper
18
2012 · Mathematics · Coordinate Geometry · Hyperbola
IIT JEE 2012 PAPER 1 OFFLINE
Tangents are drawn to the hyperbola \({{{x^2}} \over 9} - {{{y^2}} \over 4} = 1,\) parallel to the straight line \(2x - y = 1,\) The points of contact of the tangents on the hyperbola are
A
\(\left( {{9 \over {2\sqrt 2 }},{1 \over {\sqrt 2 }}} \right)\)
B
\(\left( -{{9 \over {2\sqrt 2 }},-{1 \over {\sqrt 2 }}} \right)\)
C
\(\left( {3\sqrt 3 , - 2\sqrt 2 } \right)\)
D
\(\left( -{3\sqrt 3 , 2\sqrt 2 } \right)\)
Open complete paper
19
2015 · Mathematics · Coordinate Geometry · Hyperbola
JEE ADVANCED 2015 PAPER 2 OFFLINE
Consider the hyperbola \(H:{x^2} - {y^2} = 1\) and a circle \(S\) with center \(N\left( {{x_2},0} \right)\). Suppose that \(H\) and \(S\) touch each other at a point \(P\left( {{x_1},{y_1}} \right)\) with \({{x_1} > 1}\) and \({{y_1} > 0}\). The common tangent to \(H\) and \(S\) at \(P\) intersects the \(x\)-axis at point \(M\). If \((l, m)\) is the centroid of the triangle \(PMN\), then the correct expressions(s) is(are)
A
\({{dl} \over {d{x_1}}} = 1 - {1 \over {3x_1^2}}\) for \({x_1} > 1\)
B
\({{dm} \over {d{x_1}}} = {{{x_1}} \over {3\left( {\sqrt {x_1^2 - 1} } \right)}}\) for \({x_1} > 1\)
C
\({{dl} \over {d{x_1}}} = 1 + {1 \over {3x_1^2}}\) for \({x_1} > 1\)
D
\({{dm} \over {d{y_1}}} = {1 \over 3}\) for \({y_1} > 0\)
Open complete paper
20
2017 · Mathematics · Coordinate Geometry · Hyperbola
JEE ADVANCED 2017 PAPER 1 OFFLINE
For \(a = \sqrt 2\), if a tangent is drawn to a suitable conic (Column 1) at the point of contact (\(-\)1, 1), then which of the following options is the only CORRECT combination for obtaining its equation?
A
(I) (ii) Q)
B
(I) (ii) (P)
C
(III) (i) (P)
D
(II) (ii) (Q)
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Showing 20 of 28 questions